Math Problem Statement

how did they get fcf

how did they get fcf

Solution

To calculate the Free Cash Flow (FCF) in each year, we can follow this general approach based on the data provided in the table:

Free Cash Flow (FCF) Calculation Steps

The formula used to calculate Free Cash Flow (FCF) is generally:

FCF=Taxable IncomeTax+Depreciation ExpenseCAPEX\text{FCF} = \text{Taxable Income} - \text{Tax} + \text{Depreciation Expense} - \text{CAPEX}

Breaking down for each year:

  1. Year 1:

    • Taxable Income: 0.43
    • Tax: -0.1075
    • Depreciation Expense: -0.8
    • CAPEX: -2 (since CAPEX is typically a one-time investment, it affects Year 0 and not subsequent years)

    Using the formula: FCF=0.43(0.1075)+(0.8)(2)=1.1225\text{FCF} = 0.43 - (-0.1075) + (-0.8) - (-2) = 1.1225

  2. Year 2:

    • Taxable Income: 0.63
    • Tax: -0.1575
    • Depreciation Expense: -0.6
    • CAPEX: 0 (no new CAPEX mentioned for this year)

    Using the formula: FCF=0.63(0.1575)+(0.6)=1.0725\text{FCF} = 0.63 - (-0.1575) + (-0.6) = 1.0725

  3. Year 3:

    • Taxable Income: 0.33
    • Tax: -0.0825
    • Depreciation Expense: -0.6
    • CAPEX: 0 (no new CAPEX mentioned for this year)

    Using the formula: FCF=0.33(0.0825)+(0.6)=0.8475\text{FCF} = 0.33 - (-0.0825) + (-0.6) = 0.8475

Explanation of Each Term

  • Taxable Income: The income after subtracting all operating expenses.
  • Tax: Calculated based on Taxable Income.
  • Depreciation Expense: Added back as a non-cash expense.
  • CAPEX: Deducted in Year 0 as initial investment.

Would you like further details on any specific part of this calculation?


Here are some questions to deepen your understanding:

  1. How would changes in CAPEX affect future Free Cash Flow?
  2. Why is Depreciation Expense added back in FCF calculations?
  3. What would be the impact of a higher tax rate on FCF?
  4. How is operating expense factored into the calculation of taxable income?
  5. Can you calculate FCF if CAPEX occurred in each year instead of Year 0?

Tip: Remember, CAPEX is usually a one-time or periodic investment and can greatly impact the first-year cash flows.

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Math Problem Analysis

Mathematical Concepts

Free Cash Flow (FCF) Calculation
Taxable Income
Depreciation
CAPEX

Formulas

FCF = Taxable Income - Tax + Depreciation Expense - CAPEX

Theorems

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Suitable Grade Level

College level (Finance/Accounting)